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Any linear system of point-groups on a curve with only ordinary singularities may be cut by adjoint curves.

A subset M of a Hilbert space H is a linear manifold if it is closed under addition of vectors and scalar multiplication.

Two curves phi and psi satisfying phi+psi=0 are said to be linearly dependent. Similarly, n curves phi_i, i=1, ..., n are said to be linearly dependent if sum_(i=1)^nphi_i=0.

This is proven in Rademacher and Toeplitz (1957).

A member of the smallest algebraically closed subfield L of C which is closed under the exponentiation and logarithm operations.

The study of a finite group G using the local subgroups of G. Local group theory plays a critical role in the classification theorem of finite groups.

For a given function f(x) over a partition of a given interval, the lower sum is the sum of box areas m^*Deltax_k using the infimum m of the function f(x) in each subinterval ...

If every component L of X/O_(p^')(X) satisfies the "Schreler property," then L_(p^')(Y)<=L_(p^')(X) for every p-local subgroup Y of X, where L_(p^') is the p-layer.

For an arbitrary not identically constant polynomial, the zeros of its derivatives lie in the smallest convex polygon containing the zeros of the original polynomial.

Let rho(x) be an mth degree polynomial which is nonnegative in [-1,1]. Then rho(x) can be represented in the form {[A(x)]^2+(1-x^2)[B(x)]^2 for m even; ...